Question

An automatic filling machine in a factory fills bottles of ketchup with a mean of 17.6 oz and a standard deviation of 0.05 oz with a distribution that can be well modeled by a Normal model. What is the probability that a bottle of ketchup contains less than 17.5 ​oz?

Answer 1

Answer: 0.0228

Step-by-step explanation:

Given : $\text{Mean}=\mu=17.6\ oz$

$\text{Standard deviation}=\sigma=0.05\ oz$

Since , the distribution follows a Normal distribution .

The formula to calculate the z-score is given by :-

$z=\dfrac{x-\mu}{\sigma}$

For x=17.5 oz

$z=\dfrac{17.5-17.6}{0.05}=-2$

The p-value = $P(z<-2)=0.0227501\approx0.0228$

Hence, the required probability : 0.0228